The distribution of the heights, x , in meters, of trees is represented by the d

Question

The distribution of the heights, x , in meters, of trees is represented by the density function p(x) in the figure below: Enter the exact answers. Calculate the fraction of trees which are: (a) Less than 10 meters high The fraction of trees less than meters high is (b) More than meters high The fraction of trees more than meters high is (c) Between 5 and 10 meters high The fraction of trees between 5 and 10 meters high is In this question you will evaluate the following improper integral. (a) Use the Fundamental Theorem to find . Your answer will contain b Enter the exact answer. (b) Now take the limit as b right arrow infinite.

Explanation / Answer

1)the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.

The actual value will be 1/8

When we integrate this will be general -{1}/{8x^8}

Under upper limit b and lower limit 1 ---------------------ans 1

1/8 + 1/8 b^8

taking b as infinity and lower limit as 1 --------------------ans 2

= 1/8

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